I like this euphemism for age "(ie chronologically gifted)". Despite its common use in everyday parlance, I'd avoid using old to mean previous/former around people who are particularly PC & who are prepared to take umbrage at everything they hear that might even remotely imply a negative meaning. All 5 of my "old wives" are much younger than I, except for the two who are "late". For most folks, perception is reality, even when they know it isn't (cognitive dissonance); and judgment is half of their alleged "right to freedom of expression", & self-righteous indignation, the other half.
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user21497Jan 12 '13 at 7:38

"in the provided context.": What context is provided in the question? For all purposes, the phrase could be followed by: ", not the younger one, I mean." providing the required "context".
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KrisJan 12 '13 at 7:31

Generally, old in the sense of former or previous is not used in such constructions at all. In the given context, the word old can only mean aged; My old teacher cannot be the opposite of My new teacher.

However, old is sometimes used in such expressions as my old house (to mean the previous), and an old friend (long-time friend).

On a different note, the use of old for former or previous is standard in some Oriental languages, where old is the antonym of new in every context.

"But should it be avoided in this context anyway?" Yes.

[EDIT]
The adjective applies to time (indirect, elided reference) rather than the noun mentioned (person). As such, it can be used only where its reference is unambiguously to time. "My old friend" has the elision: "My old (-time) friend". Not all contexts are self-explanatory and can be ambiguous, as in "My old teacher" occurring without context.

Kris, I have to say that it was quite a common expression for former where I grew up (New York State) as in: "When I went back for my class reunion I got to see many of my old teachers." Also here it is used in a book
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JimJan 12 '13 at 5:45

@Jim "When I went back for my class reunion I got to see many of my old teachers." refers to teachers of the old (earlier times) not the previous (as opposed to current). So is the use of old teacher in the book as well.
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KrisJan 12 '13 at 5:51

1

I guess I don't see any difference between previous and of an earlier time because I don't interpret previous to mean exactly one prior, it could be any one of my former teachers. Could you explain how you see it as different?
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JimJan 12 '13 at 5:55

The insistence by @Kris that "previous" can only mean immediately prior rather ignores the fact that the OP asked asked about previous or former. My former students referred to me as their "old teacher" long before the second meaning (aged) was applicable.
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FortiterJan 12 '13 at 7:17